Problem: Express this product in scientific notation: $(8.70\times 10^{5})\times (5.00\times 10^{5})$
Solution: Start by collecting like terms together. $= (8.70\times 5.00) \times (10^{5}\times 10^{5})$ When multiplying exponents with the same base, add the powers together. $= 43.5 \times 10^{5\,+\,5}$ $= 43.5 \times 10^{10}$ To write the answer correctly in scientific notation, the first number needs to be between $1$ and $10$ . In this case, we need to move the decimal one position to the left without changing the value of our answer. $ $ We can use the fact that $43.5$ is the same as $4.350 \times 10$ $ = {4.350 \times 10} \times 10^{10} $ $= 4.350\times 10^{11}$